Nodal solutions for the Choquard equation

We consider the general Choquard equations [GRAPHICS] where I-alpha is a Riesz potential. We construct minimal action odd solutions for p is an element of (N+alpha/N, N+alpha/N-2) and minimal action nodal solutions for p is an element of (2, N+alpha/N-2) We introduce a new minimax principle for least action nodal solutions and we develop new concentration compactness lemmas for sign-changing Palais-Smale sequences. The nonlinear Schrodinger equation, which is the nonlocal counterpart of the Choquard equation, does not have such solutions. (C) 2016 Elsevier Inc. All rights reserved.